Multi-wavelength Intra-day Variability and Quasi-periodic Oscillation in Blazars

We reviewed multi-wavelength blazars variability and detection of quasi-periodic oscillations on intra-day timescales. The variability timescale from few minutes to up to less than a days is commonly known as intra-day variability. These fast variations are extremely useful to constrain the size of emitting region, black hole mass estimation, etc. It is noticed that in general blazars show intra-day variability in the complete electromagnetic spectrum. But some class of blazars either do not show or show very little intra-day variability in a specific band of electromagnetic spectrum. Blazars show rarely quasi-periodic oscillations in time series data in optical and X-ray bands. Other properties and emission mechanism of blazars are also briefly discussed.Comment: Invited Review; Submitted to Galaxies; a special issue on Microvariability of Blazar

On decoding of multi-level MPSK modulation codes

The decoding problem of multi-level block modulation codes is investigated. The hardware design of soft-decision Viterbi decoder for some short length 8-PSK block modulation codes is presented. An effective way to reduce the hardware complexity of the decoder by reducing the branch metric and path metric, using a non-uniform floating-point to integer mapping scheme, is proposed and discussed. The simulation results of the design are presented. The multi-stage decoding (MSD) of multi-level modulation codes is also investigated. The cases of soft-decision and hard-decision MSD are considered and their performance are evaluated for several codes of different lengths and different minimum squared Euclidean distances. It is shown that the soft-decision MSD reduces the decoding complexity drastically and it is suboptimum. The hard-decision MSD further simplifies the decoding while still maintaining a reasonable coding gain over the uncoded system, if the component codes are chosen properly. Finally, some basic 3-level 8-PSK modulation codes using BCH codes as component codes are constructed and their coding gains are found for hard decision multistage decoding

X-ray Intraday Variability of Five TeV Blazars with NuSTAR

We have examined 40 NuSTAR light curves (LCs) of five TeV emitting high synchrotron peaked blazars: 1ES 0229+200, Mrk 421, Mrk 501, 1ES 1959+650 and PKS 2155-304. Four of the blazars showed intraday variability in the NuSTAR energy range of 3-79 keV. Using an auto correlation function analysis we searched for intraday variability timescales in these LCs and found indications of several between 2.5 and 32.8 ks in eight LCs of Mrk 421, a timescale around 8.0 ks for one LC of Mrk 501, and timescales of 29.6 ks and 57.4 ks in two LCs of PKS 2155-304. The other two blazars' LCs do not show any evidence for intraday variability timescales shorter than the lengths of those observations, however, the data was both sparser and noisier, for them. We found positive correlations with zero lag between soft (3-10 keV) and hard (10-79 keV) bands for most of the LCs, indicating that their emissions originate from the same electron population. We examined spectral variability using a hardness ratio analysis and noticed a general "harder-when-brighter" behavior. The 22 LCs of Mrk 421 observed between July 2012 and April 2013 show that this source was in a quiescent state for an extended period of time and then underwent an unprecedented double peaked outburst while monitored on a daily basis during 10 - 16 April 2013. We briefly discuss models capable of explaining these blazar emissions.Comment: 21 pages, 4 figures, 4 tables, Accepted for Publication in Ap

Multi-wavelength Temporal Variability of the Blazar 3C 454.3 during 2014 Activity Phase

We present a multi-wavelength temporal analysis of the blazar 3C 454.3 during the high $\gamma$-ray active period from May-December, 2014. Except for X-rays, the period is well sampled at near-infrared (NIR)-optical by the \emph{SMARTS} facility and the source is detected continuously on daily timescale in the \emph{Fermi}-LAT $\gamma$-ray band. The source exhibits diverse levels of variability with many flaring/active states in the continuously sampled $\gamma$-ray light curve which are also reflected in the NIR-optical light curves and the sparsely sampled X-ray light curve by the \emph{Swift}-XRT. Multi-band correlation analysis of this continuous segment during different activity periods shows a change of state from no lags between IR and $\gamma$-ray, optical and $\gamma$-ray, and IR and optical to a state where $\gamma$-ray lags the IR/optical by $\sim$3 days. The results are consistent with the previous studies of the same during various $\gamma$-ray flaring and active episodes of the source. This consistency, in turn, suggests an extended localized emission region with almost similar conditions during various $\gamma$-ray activity states. On the other hand, the delay of $\gamma$-ray with respect to IR/optical and a trend similar to IR/optical in X-rays along with strong broadband correlations favor magnetic field related origin with X-ray and $\gamma$-ray being inverse Comptonized of IR/optical photons and external radiation field, respectively.Comment: 15 pages, 5 figures, 1 table, MNRAS accepte

Model Uncertainty and its Impact on Derivative Pricing

Financial derivatives written on an underlying can normally be priced and hedged accurately only after a suitable mathematical model for the underlying has been determined. This chapter explains the difficulties in finding a (unique) realistic model \u2014 model uncertainty. If the wrong model is chosen for pricing and hedging, unexpected and unwelcome financial consequences may occur. By wrong model we mean either the wrong model type (specification\ud uncertainty) or the wrong model parameter (parameter uncertainty). In both cases, the impact of model uncertainty on pricing and hedging is significant. A variety of measures are introduced to value the model uncertainty of derivatives and a numerical example again confirms that these values are a significant proportion of the derivative price